House Republicans can’t shake their identity crisis. Their struggle over how and whether to push an immigration bill continues to plague an already divided party.

The party’s establishment wing is hinting it wants to vote on some aspect of the issue before the midterm elections. But hardcore conservatives, angry with Speaker John Boehner, R-Ohio, for mocking their tactics in a speech last month, have vowed to be vigilant against letting any kind of distasteful legislation slip through to the floor.

“I hope he learned a lesson,” Rep. Raul Labrador, R-Idaho, once a devoted supporter of a comprehensive solution, said about Boehner’s remarks. Labrador has emerged as one of Boehner’s most vocal critics on immigration.

The GOP’s uncertainty over immigration reflects the mood of a party continuing to grapple with who it is and what it wants to become.

Leaders want to appeal to the broader, more diverse and rapidly growing voter bloc of Latinos. Others want to protect the interest of their many voters, who see legalization for undocumented immigrants as an affront to the rule of law.

Latinos currently make up 11.8 percent of all eligible voters. But they’re growing fast, as a half-million new potential voters become eligible each year after turning 18 or becoming naturalized citizens, according to surveys by Latino Decisions, a Latino political opinion research organization.

The Pew Research Center found in a February survey that 72 percent of Hispanics said it was very or extremely important this year to have new immigration legislation. Forty-four percent of whites and 49 percent of blacks agreed.

Establishment figures feel something has to be done before the midterm elections. Appearing too doctrinaire could cost votes, warned Rep. Mike Simpson, R-Idaho, who is close to Boehner.

“They want a solution. They want reasonableness,” he said of voters.

A mass legalization bill is out of the question this year, said Labrador, but he thinks the House of Representatives could pass a couple of smaller bills that move the process forward.

Tougher border security and a guest-worker program appear to be the strongest prospects for gaining consensus.

Vice President Joe Biden used an event Monday that celebrated Cinco de Mayo as a platform to press Boehner to stand up to other Republicans and bring a vote to the floor.

“It's time for him to stand up, stand up at not let the minority _ I think it’s a minority _ of the Republican Party in the House keep us from moving in a way that will change the circumstances for millions and millions of lives,” Biden said.

Biden didn’t back down from earlier statements he has made this spring referring to those here illegally as “already Americans.” They may not be citizens, Biden said, but they’re Americans, according to standards outlined by former President Theodore Roosevelt.

“Americanism is not a question of birthplace or creed or line of descent, it’s a question of principles, idealism and character,” Biden said. “And I would argue that those 11 million folks who have been here breaking their neck, working hard, they are Americans.”

Since taking office, President Barack Obama has deported more immigrants, 2 million, than any other president, even though he has not finished his second term. Yet he stoked the debate in March when he instructed his secretary of homeland security to search for ways to reduce deportations. Some Republicans saw this as a sign his next move could be an executive order blocking more deportations.

Since then, a growing chorus of Republicans has been speaking out in favor of an immigration overhaul, including the former chairman of the House Homeland Security Committee, Rep. Peter King of New York, and Illinois Rep. Aaron Schock.

Republican supporters of moving forward on immigration face at least two intra-party hurdles. One is that many Republican districts and states have small immigrant populations. The other: Republicans don’t want to take the political focus off Obama, notably because of his unpopular health care program.

Business supporters have turned up their lobbying efforts, launching a television ad campaign this week highlighting several inventions, including hairdryers and Google, created by immigrants.

Most primaries are over by the Fourth of July, so business leaders see the next several weeks as the last, best opportunity to slip in legislation that would allow them to legally hire more foreign workers before year’s end.

Jeremy Robbins, executive director of the Partnership for a New American Economy, a business-minded immigration advocacy group started by former New York Mayor Michael Bloomberg, said the political climate for immigration legislation has improved, and that the concerns some supporters of immigration may have had about challenges from the right have not materialized.

He pointed to Texas Republican Reps. John Carter and Sam Johnson, both of whom were part of bipartisan efforts to pass a comprehensive overhaul. Carter didn’t face a primary challenger. Johnson won his March 4 primary by more than 80 percent.

Many supporters will have their eyes on Republican Rep. Renee Ellmers during the North Carolina primary May 6. Ellmers has taken some political hits for her support of an immigration overhaul that would allow people here illegally to remain. Her challenger, Frank Roche, has made it the top issue of his campaign.

During a heated interview with Ellmers in March, conservative radio host Laura Ingraham accused the lawmaker of supporting “de facto amnesty.” Ellmers said Ingraham had an “ignorant position.”

Hispanic votes are difference makers in key presidential election states, making up at least 14 percent of the vote in Colorado, Florida, Nevada, Arizona and New Mexico.

That doesn’t account for eligible voters who are not yet registered. In Texas, for example, there are an estimated 2.1 million eligible Latino voters who are not yet registered, according to Latino Decisions. In California, there are another 2 million eligible Latinos who are not registered. In Florida, it’s more than 600,000.

“Not to act would be devastating for the party politically. You’d polarize the Hispanic electorate,” said Sen. John McCain, R-Ariz., a longtime advocate of comprehensive immigration legislation.

Boehner has signaled a willingness to consider voting on changes to immigration law. When Republicans met at a Cambridge, Md., retreat in January, he offered a framework for action, notably allowing undocumented workers to remain in the country, but not as citizens.

Conservative Republicans wouldn’t buy it, and plans were put on hold. Then on April 24, Boehner seemed to mock his wary colleagues.

In a speech to the Rotary Club of Middletown, Ohio, Boehner said of fellow House members, “Here’s the attitude: ‘Ohhhh. Don’t make me do this. Ohhhh. This is too hard,’” according to a Cincinnati Enquirer report.

“We get elected to make choices. We get elected to solve problems, and it’s remarkable to me how many of my colleagues just don’t want to. . . . They’ll take the path of least resistance,” Boehner said in the speech.

Labrador said the remarks did more harm than good by shifting blame to House Republicans and away from Obama, who Labrador said has failed to work with Republicans.

Tuesday, after House Republicans met for their weekly Capitol caucus, Boehner characterized his Rotary Club remarks as good-natured kidding. “There was no mocking,” he told reporters. “You all know me. You know, you tease the ones you love, right?”

Boehner reiterated that he would keep working with members to find areas of agreement, and he insisted “the biggest impediment we have moving immigration reform is that the American people don’t trust the president to enforce or implement the law that we may or may not pass.”